Geometric Scattering Theory [Paperback]

These lecture notes are intended as a non-technical overview of scattering theory.This overview of geometric scattering theory shows how it provides a parametrization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. It will be of interest to graduate students and researchers in mathematics and engineering.This overview of geometric scattering theory shows how it provides a parametrization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. It will be of interest to graduate students and researchers in mathematics and engineering.This book is an overview of scattering theory. The author shows how this theory provides a parametrization of the continuous spectrum of an elliptic operator on a complete manifold with uniform structure at infinity. In the first two lectures the author describes the simple and fundamental case of the Laplacian on Euclidean space to introduce the theory's basic framework. In the next three lectures, he outlines various results on Euclidean scattering, and the methods used to prove them. In the last three lectures he extends these ideas to non-Euclidean settings.List of illustrations; Introduction; 1. Euclidean Laplacian; 2. Potential scattering on Rn; 3. Inverse scattering; 4. Trace formulae and scattering poles; 5. Obstacle scattering; 6. Scattering metrics; 7. Cylindrical ends; 8. Hyperbolic metrics.' & overall the book is of interest for students and researchers if they wish to obtain an overview of this theory.' O. R?schel, International Mathematical News